Choosing a statistical test

When choosing a statistical test it is important that you known what you want to test. When doing a specific statistical test and it is significant it is important to verify the shape and and the sample size. For more information what are the restrictions of each test see the specific page of the test.

Ratio and Interval Scale

• Mean/Median
• Variation
• Linear relations
• Reliability failure rate
• Shape of distribution
• Analysis of a measurement system
• Overview

Mean or Median

Difference Mean or Median and a hypothetic value

• Normal Distribution one sample t-test
• Not Normal Distribution 1 sample Wilcoxon median test

Difference between 2 Means or Medians

• Normal Distribution 2 sample t-test
• Not Normal Distribution 1 sample Wilcoxon median test

Difference between multiple Means or Medians

• Normal Distribution One way Anova
• Not Normal Distribution Kruskal-Wallis Test

Variation

Difference between 2 variations

• Normal Distribution Variation F-test
• Not Normal Distribution Variation Levene test

Difference between multiple variations

• Normally and Not Normal Distribution Variation Levene test

Linear relations

Relations between 2 data-sets

• Correlation calculates if there is a relation
• Regression calculates what the relations is between the data-sets

Relations between multiple data-sets

• multiple correlation coefficient calculates if there is a relation
• Multiple linear regression calculates what the relations is between the data-sets

Reliability failure rate

• Beta know small sample size Weibayes
• Big samples size Weibull analysis (n>20)

Shape of distribution

• Distribution fitting
• Anderson Darling normality test
• Skewness
• Kurtosis

Analysis of a measurement system

• Non Destructive testing Crossed Gauge R&R
• Destructive testing Nested Gauge R&R (destructive)

Overview

Test what	Normal Distribution	With what statistical test
Difference in Mean/Median	Yes	t-test
	No	Wilcoxon–Mann–Whitney-test
Difference in Mean/Median between multiple data sets	Yes	One way Anova
	No	Kruskal-Wallis Test
Difference in Variation	Yes	Variation F-test
	No	Variation Levene test
If data set is normal distributed	n.a.	Anderson Darling normality test
Is the data according specification	Yes	Cp Cpk % out of tolerance
If there is relation between two data sets	n.a.	Correlation
Calculates the relation between data sets	n.a	Regression
Difference in two proportions (Data set with only good or false results)	n.a.	Proportions